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作者：Camerlenghi, Federico; Lijoi, Antonio; Orbanz, Peter; Prunster, Igor
作者单位：University of Milano-Bicocca; Bocconi University; Bocconi University; Columbia University
摘要：Hierarchies of discrete probability measures are remarkably popular as nonparametric priors in applications, arguably due to two key properties: (i) they naturally represent multiple heterogeneous populations; (ii) they produce ties across populations, resulting in a shrinkage property often described as sharing of information. In this paper, we establish a distribution theory for hierarchical random measures that are generated via normalization, thus encompassing both the hierarchical Dirichl...
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作者：Dasgupta, Sayan; Goldberg, Yair; Kosorok, Michael R.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Haifa
摘要：We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features. We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions. We present a few case studies to show that the assumptions are met in most practical situations and present simulation results to demonstrate performance of the proposed approach.
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作者：Lepski, O., V; Willer, T.
作者单位：Aix-Marseille Universite
摘要：We study the problem of nonparametric estimation under L-p-loss, p is an element of[1, infinity), in the framework of the convolution structure density model on R-d. This observation scheme is a generalization of two classical statistical models, namely density estimation under direct and indirect observations. The original pointwise selection rule from a family of kernel-type estimators is proposed. For the selected estimator, we prove an L-p-norm oracle inequality and several of its conseque...
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作者：Lin, Zhenhua; Yao, Fang
作者单位：National University of Singapore; Peking University
摘要：In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen-Loeve expansion for Riemannian random processes. This framework also features an approach to compare objects from different tensor Hilbert spaces, which paves the way for asymptotic analysis in Riemannian functional data analysis. Built upon intrinsic geometric c...
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作者：Zheng, Shurong; Chen, Zhao; Cui, Hengjian; Li, Runze
作者单位：Northeast Normal University - China; Northeast Normal University - China; Capital Normal University; Fudan University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with test of significance on high-dimensional covariance structures, and aims to develop a unified framework for testing commonly used linear covariance structures. We first construct a consistent estimator for parameters involved in the linear covariance structure, and then develop two tests for the linear covariance structures based on entropy loss and quadratic loss used for covariance matrix estimation. To study the asymptotic properties of the proposed tests, we st...
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作者：Bodnar, Taras; Dette, Holger; Parolya, Nestor
作者单位：Stockholm University; Ruhr University Bochum; Leibniz University Hannover
摘要：In this paper, new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diagonal covariance matrix. The asymptotic properties of the new test statistics are investigated under the null hypothesis and the alternative hypothesis using random matrix theory. For this purpose, we study the weak conv...
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作者：Chetelat, Didier; Wells, Martin T.
作者单位：Universite de Montreal; Polytechnique Montreal; Cornell University
摘要：We study the behavior of a real p-dimensional Wishart random matrix with n degrees of freedom when n, p -> infinity but p/n -> 0. We establish the existence of phase transitions when p grows at the order n((K+1)/(K+3)) for every K is an element of N, and derive expressions for approximating densities between every two phase transitions. To do this, we make use of a novel tool we call the F-conjugate of an absolutely continuous distribution, which is obtained from the Fourier transform of the s...
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作者：Balakrishnan, Sivaraman; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or unbounded number of categories. In the continuous case, we consider testing a Holder density with exponent 0 < s <= 1, with possibly unbounded support, in the low-smoothness reg...
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作者：Williams, Jonathan P.; Hannig, Jan
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design matrix is collinear. To overcome this challenge, an entirely new perspective on variable selection is presented within a generalized fiducial inference framework. This new procedure is able to effectively account for linear dependencies among subsets of cova...
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作者：Neykov, Matey; Lu, Junwei; Liu, Han
作者单位：Carnegie Mellon University; Princeton University; Northwestern University; Northwestern University
摘要：We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global structure of the underlying graph. Examples include testing the graph connectivity, the presence of a cycle of certain size, or the maximum degree of the graph. To begin with, we study the information-theoretic limits of a large family of combinatorial inferen...
